Question

已知x+y=6,xy=4,x>y则√x-√y/√x+√y

Answer 1

√x-√y/√x+√y

=（√x-√y）(√x+√y)/(√x+√y)²

=(x-y)/(x+y+2√xy)

=（x-y)/(6+2√4)

=(x-y)/10

x＞y,x-y=√(x-y)²=√[(x+y)²-4xy]=√(6²-16)=√20=2√5

∴√x-√y/√x+√y=2√5/10=√5/5

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